In quantum case \(T(\lambda )\)  becomes the transfer matrix, which is related to qKdV charges via an asymptotic expansion [1]}
\(\ln T &=& \kappa \, \mu ^{1/2}\, {\rm 1} -\sum _{n} C_n\, \mu ^{1/2-n}\, Q_{2n-1},\quad \mu \rightarrow \infty ,\) 
